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This paper addresses a gap in the classifcation of Codazzi tensors withexactly two eigenfunctions on a Riemannian manifold of dimension three orhigher. Derdzinski proved that if the trace of such a tensor is constant andthe dimension of one of the the eigenspaces is $n-1$, then the metric is awarped product where the base is an open interval- a conclusion we will show tobe true under a milder trace condition. Furthermore, we construct examples ofCodazzi tensors having two eigenvalue functions, one of which has eigenspacedimension $n-1$, where the metric is not a warped product with interval base,refuting a remark in \cite{Besse} that the warped product conclusion holdswithout any restriction on the trace.

Codazzi Tensors with Two Eigenvalue Functions